On computing transports in finite-element models

Local volume and tracer balances in finite-element models which use continuous shape functions for elevation and tracers are written for patches of elements. Although the locally conserving nodal fluxes can be introduced at the postprocessing stage, they generally lead to an ambiguous definition of transports between two points of the computational mesh and are frequently impractical. Practical computation of transports involves either re-projection or interpolation which, in turn, causes imbalances. The output of Finite Element Ocean circulation Model run on several meshes including the North Atlantic is used to illustrate the ambiguities in transport computations. Simple approximate ways of estimating transports are also discussed. It is shown that imbalances/ambiguities can be significant on coarse (about one degree) unstructured meshes reaching several Sverdrups (106 m3/s). This may hamper studies of ocean variability unless appropriate resolution is used.